Field of the Invention
This invention relates to improved composite piezoelectric materials which find use in ultrasonic applications such as transducers used in naval sonar and in medical ultrasonic imagers. Piezoelectric materials are also used to achieve hydrostatic electromechanical coupling which characteristic can be used in passive hydrophones. In addition, numerous other applications of piezoelectric materials have been developed as electromechanical and electroacoustic transducers.
Although single crystal piezoelectric materials retain their utility and dominate certain special arenas, such as frequency stabilized oscillators, in applications ranging from watches to radar, and surface acoustic wave devices, in applications ranging from television filters to analogue signal correlators, new piezoelectric materials combining a piezoelectric ceramic with a passive polymer have now come to the forefront of the market. Our invention relates to these newer piezoceramic composites and their numerous uses. In particular, our invention contemplates the use of negative Poisson's ratio materials as the passive polymer in the composite structure.
The key consideration in the design; whether for a sensor, an actuator, or both simultaneously; is to ensure the maximum efficiency in electromechanical energy conversion. There are many engineering applications' demands--weight, flexibility, environmental stability, electrical impedance matching, acoustic radiation coupling, cost--that will pull the design away from this optimum, but it is best to aim first at the right target. There are usually many ways to compensate for the piezomaterial's shortfalls in meeting design criteria other than electromechanical energy conversion: acoustic matching layers, electrical transformers, environmental coatings, buoyant ballast. But the piezoelectric material is the only place where electromechanical energy transformation is accomplished. Maximizing the composite's electromechanical coupling should be the first aim in the piezocomposite material design.
In pulse-echo applications, a rod composite piezoelectric is more effective at electromechanical energy conversion than is its constituent piezoceramic. While this seems counter-intuitive at first blush, a quick glance at FIG. 2 clarifies the issue. That figure depicts in cross-section the response of a thin composite plate to a high frequency pressure wave impinging on its faces. At the high frequencies employed in pulse-echo applications, the thin plate is so wide that it is inertially clamped as a whole in the lateral directions. That is, the pressure on the faces reverses so fast that the plate does not have time to bulge or contract in the sideways direction. This lateral clamping reduces the total displacement and total piezoelectric charge produced in a solid plate of piezoceramic. In the piezocomposite structure, however, the thin ceramic rods are free to expand or contract in the sideways direction at the expense of the much softer polymer which surrounds them. A piezocomposite plate can have a thickness-mode electromechanical coupling constant (.about.60-70%), much larger than the thickness-mode coupling of a solid ceramic plate (.about.45-50%), approaching even the coupling of a long ceramic rod (.about.70-75%). FIG. 3 shows how the thickness-mode coupling constant for a composite plate varies with volume fraction of piezoceramic for three different polymers. The composite's thickness mode coupling exceeds that of the component ceramic for all but the lowest volume fractions; moreover, a softer polymer permits higher values.
In hydrostatic applications, the effectiveness of a piezoelectric material for electromechanical energy-conversion is measured by the hydrostatic coupling coefficient, EQU k.sub.h =d.sub.h /(.epsilon..sub.33.sup.T S.sub.h.sup.E).sup.1/2
where d.sub.h is the material's hydrostatic current responsivity, .epsilon..sub.33.sup.T its dielectric permittivity, and s.sub.h.sup.E the material's hydrostatic compliance.
The hydrostatic current responsivity, d.sub.h =d.sub.33 +2d.sub.31, has two contributions--one from pressure on the faces of the plate, d.sub.33, and the other from pressure on the sides, d.sub.31. These two contributions are typically of opposite sign and nearly equal in magnitude. In the piezocomposites, we can increase d.sub.h by reducing the negative lateral contributions.
FIG. 4A depicts the contribution to the hydrostatic current responsivity of the composite from the force exerted on the faces of the plate. The effect is similar to the uniaxial response shown in FIG. 2 above except that, at low frequencies, the entire plate is free to expand laterally. The essential role of the polymer is to transfer the force falling on it to the adjacent ceramic. The d.sub.33 of the composite is nearly equal to the d.sub.33 of the constituent piezoceramic since nearly all the force falling on the plate is transferred to the ceramic.
A top view of the composite plate is shown in FIG. 4B which portrays a portion of the contribution to the hydrostatic current responsivity from the force exerted on the sides of the composite plate. Here the polymer transfers part of the lateral force to the ceramic and bears part of the lateral force itself in the regions between the piezoceramic rods. To reduce these negative contributions to the hydrostatic response, we can add reinforcing fibers to these polymer paths so that more of the lateral force is borne by the piezoelectrically passive part of the structure.
A side view of the composite plate in FIG. 4C which shows the remaining portion of the contribution to the hydrostatic current responsivity from the force exerted on the sides of the composite plate. Here the polymer both presses on the sides of the ceramic rods as well as bulges up. The direct pressure on the sides of the ceramic was accounted for above. The bulging of the polymer, however, is a new effect. This bulging causes the polymer to pull on the ceramic rods trying to lengthen them, thereby producing a contribution to the d.sub.31 of the composite from the d.sub.33 of the ceramic. This Poisson-ratio effect is an important contribution to the composite's d.sub.31. To minimize this contribution to the composite's d.sub.31 we can reduce the polymer's Poisson ratio by adding air bubbles. Foaming the polymer is an effective strategy for reducing these deleterious contributions to the hydrostatic response, but unfortunately introduces an unwanted pressure dependence because these air pockets can collapse under high static bias pressures.
FIG. 5A shows that the d.sub.33 coefficient rises monotonically with ceramic fraction: as the amount of ceramic increases, more of the force on the faces of the plate is borne by the piezoelectrically active ceramic and less by the passive polymer. Since ceramics are typically an order of magnitude stiffer than the polymer, the composite's d.sub.33 attains almost the value of the ceramic's d.sub.33 already at low ceramic fraction. At low ceramic content, the more stiff the ceramic, the greater fraction of the force on the ceramic. At moderate ceramic content, the shifting of the load from the polymer to the ceramic saturates and little more remains to be gained since once the ceramic is carrying most of the external force, it can do no more.
The curves of FIG. 5B show the variation of the composite's d.sub.31 coefficient in the solid curve, as well as, in the dotted curves, the two contributions that sum up to it, namely, d.sub.31 =.alpha.d.sub.31 +.beta.d.sub.33, where the .alpha.d.sub.31 term is the contribution from the ceramic's d.sub.31, and .beta.d.sub.33 term contains the contribution from the ceramic's d.sub.33. The enhancement of the composite's d.sub.31 by the .beta.d.sub.33 term is deleterious. It stems from the stress on the composite's sides causing the more compliant polymer to bulge vertically more than the ceramic; the bulging polymer acts to extend the rods, producing a charge directly from the ceramic's d.sub.33.
The curve in FIG. 5C shows the composite's hydrostatic charge response, d.sub.h =d.sub.33 +2d.sub.33, which is just the sum of the two previously described curves. The composite structure enhances d.sub.h over the ceramic's d.sub.h at low volume fraction.
While the piezoelectric coefficient--discussed above--is central to the use of piezocomposites as hydrostatic transducer materials, other properties of the material are important in determining their suitability for devices, in particular their dielectric and elastic coefficients. FIG. 6 shows the variation with ceramic fraction of the dielectric permittivity, .epsilon..sub.33.sup.T, and the hydrostatic compliance, S.sub.h.sup.E. Both of these properties interpolate nearly linearly between the values for the pure polymer and pure ceramic. In the case of the dielectric constant, the slight suppression at low ceramic fraction is due to partial mechanical clamping of the ceramic by the softer--but greater in amount--polymer. In the elastic arena, a modest curvature occurs at low ceramic fraction; this stems from the effectiveness of small amounts of ceramic in stiffening the composite plate in the direction along the rods. Combining the previously calculated hydrostatic charge coefficient, dhd h, with these elastic and dielectric responses yields the hydrostatic electromechanical coupling constant which reveals the advantage of the composite structure, namely, the composite's k.sub.h exceeds the ceramic's k.sub.h.